No privileged frame of reference

As I understand it, Einstein's dismissal of the "luminiferous aether" was based on his discovery that there is no universal frame of reference, i.e. that no frame of reference is privileged in relation to all other frames. My question is whether this principle can also be stated in the inverse, namely that all frames of reference are privileged in relation to events that take place within themselves.

(1) No frame of reference is privileged in relation to all other frames.

In Einstein's thought experiment of the train passing the embankment, the lightning bolts take place within the frame of the embankment, not the train. Does this privilege the embankment frame when measuring the timing of lightning strikes? And if not, why not?

In Einstein's thought experiment of the train passing the embankment, the lightning bolts take place within the frame of the embankment, not the train.

All events take place in all frames. They just have different coordinate values in the different frames. So when we say the lightning bolts take place within the frame of the embankment, we just mean that the coordinates that define when they happened are defined according to the frame in which the embankment is at rest. We can use the Lorentz Transformation process to see what the coordinate values are in the frame in which the train is at rest or we can pick any other frame and see what the coordinate values would be in them. No frame is privileged. Therefore, no set of coordinate values is privileged, except in the sense that we have to start with one in order to describe the situation to begin with.

Does this privilege the embankment frame when measuring the timing of lightning strikes? And if not, why not?

When you are setting up and defining a scenario, you pick a frame in which to define when things happen, not measure them. Einstein could have started with the frame in which the train was at rest and defined a timing according to its coordinates but it might be a different scenario.

Staff: Mentor

In Einstein's thought experiment of the train passing the embankment, the lightning bolts take place within the frame of the embankment, not the train. Does this privilege the embankment frame when measuring the timing of lightning strikes? And if not, why not?

Events do NOT "take place in frames", although you will often find people using that wording because it's convenient. But what's really going on is that events happen, and then we use frames to assign time and space coordinates to them.

In this case, the lightning hit the embankment and left a scorch mark on it. Using a frame in which the embankment is at rest, I will measure of the speed of the scorch mark as zero; using a frame in which the train is at rest I will measure the speed of the scorch mark as (the negative of) the speed of the train relative to the embankment; and someone watching through a telescope from Mars will measure the speed of the scorch mark to be somewhere around three miles/second, depending on where Earth and Mars are in their orbits.

None of these frames are "more privileged" than any of the others. You can choose whichever one is most convenient to work with.

Staff: Mentor

In Einstein's thought experiment of the train passing the embankment, the lightning bolts take place within the frame of the embankment, not the train.

As ghwellsjr has already explained, events do not take place within a frame. They exist in all frames.

Does this privilege the embankment frame when measuring the timing of lightning strikes?

The only thing special about the embankment frame in Einstein's example is that things were set up so that the lightning strikes were simultaneous in that frame. In other frames, such as that of the train, the strikes are not simultaneous. Beyond defining the set up, there's nothing privileged about either frame.

When you are setting up and defining a scenario, you pick a frame in which to define when things happen, not measure them. Einstein could have started with the frame in which the train was at rest and defined a timing according to its coordinates but it might be a different scenario.

Okay, let's take a scenario in which the train frame is at rest. If a light flashes in the center of the train, in the train frame the light reaches the front and back of the train simultaneously. In the embankment frame, the motion of the train causes the light to reach the back slightly ahead of the front. We have a discrepancy in the timing of the light reaching the front and back of the train. Since the events in question take place in the train, why not conclude that they occur in the train frame? And if this is the case, why not conclude that the measurement of the timing of events in the train frame is definitive while the measurement in the embankment frame is distorted due to the motion of the train?

Whichever frame is at rest relative to the disputed events, isn't this the frame in which the events take place?

When you are setting up and defining a scenario, you pick a frame in which to define when things happen, not measure them. Einstein could have started with the frame in which the train was at rest and defined a timing according to its coordinates but it might be a different scenario.

Okay, let's take a scenario in which the train frame is at rest. If a light flashes in the center of the train, in the train frame the light reaches the front and back of the train simultaneously.

Only because that is what the definition of "simultaneously" is. Otherwise, we cannot know whether the light "really" arrived at the same time or not.

In the embankment frame, the motion of the train causes the light to reach the back slightly ahead of the front. We have a discrepancy in the timing of the light reaching the front and back of the train. Since the events in question take place in the train, why not conclude that they occur in the train frame? And if this is the case, why not conclude that the measurement of the timing of events in the train frame is definitive while the measurement in the embankment frame is distorted due to the motion of the train?

You cannot measure the timing of remote events until after you define what that timing is. And then you will get whatever answer you defined the timing to be when you make a subsequent "measurement".

Staff: Mentor

Since the events in question take place in the train, why not conclude that they occur in the train frame?

Again, the lightning strikes occur in every frame. The observers on the embankment see the same lightning strikes that the train observers do.

And if this is the case, why not conclude that the measurement of the timing of events in the train frame is definitive while the measurement in the embankment frame is distorted due to the motion of the train?

Why in the world would someone in the embankment frame, with their perfectly good and synchronized clocks, ignore what they measure with their own instruments?

You cannot "wish away" relativistic effects by ignoring them. The smart thing is to understand why different frames measure different times for the strikes.

Whichever frame is at rest relative to the disputed events, isn't this the frame in which the events take place?

"Events" are not things that move, like trains and such, so it doesn't make sense to talk about an event being at rest relative to something. And event is just something that happens at a particular point in space and time.

...why not conclude that the measurement of the timing of events in the train frame is definitive while the measurement in the embankment frame is distorted due to the motion of the train?

I'm sure you don't realize this, but claiming that the timing of events in one frame is definitive while in another frame is distorted, can only be true if you believe in a privileged frame, such as a "luminiferous aether" and that you can identify which frame it is.

...why not conclude that the measurement of the timing of events in the train frame is definitive while the measurement in the embankment frame is distorted due to the motion of the train?

Another way to look at this is that prior to Einstein, most scientists believed in a "luminiferous aether"--they just were unable to identify it. As such, they believed that timing was definitive only when at rest in that "luminiferous aether" rest frame but they assumed that we on the surface of the earth must be traveling in that rest frame and so our timing measurements must be distorted, although they never knew by how much. Einstein's brilliance was to note that even if there were a "luminiferous aether" rest frame that we were traveling through, we could still define our inertial rest frame to have all the characteristics of a "luminiferous aether" rest frame so that our timing measurements were definitive while timing measurement made at rest in the elusive "luminiferous aether" would be "distorted". In other words, it didn't matter whether there really was a "luminiferous aether" or not, we can define our own inertial rest frame and everything will work out just fine.

As I understand it, Einstein's dismissal of the "luminiferous aether" was based on his discovery that there is no universal frame of reference, i.e. that no frame of reference is privileged in relation to all other frames. My question is whether this principle can also be stated in the inverse, namely that all frames of reference are privileged in relation to events that take place within themselves.

(1) No frame of reference is privileged in relation to all other frames.

(2) All frames of reference are privileged in relation to themselves.

Is (1) ⇔ (2)?

emd, you are actually onto something here. I think your probing into this is best approached by first understanding that there are at least two different prominent interpretations of relativistic effects. Sometimes it helps to understand these models for relativity, then first work through your question in the context of one model, then the other model. Without a model in mind the discussion gets hazy.

The responses you've been getting here implicitly assume a model representing a universe that is 3-dimensional evolving in time. You can only get a mathematical explanation out of this model with no direct physical sense to be made of it, other than "that's just the way it works" with no further sense to be made of it.

Also, the discussions in this context tend to focus on single events rather than clarifying what's going on with extended collections of objects taken as an identifiable 3-dimensional group of objects. It's easy to visualize a single point event as not having any preferable frame. Wolfgang Rindler's text book deals with this, defining a geometric equation over a range of values in a way that does give significance to a particular frame.

My impression is that the equal validity of all frames of reference applies only in the abstract. In practice, one frame is always privileged, specifically the frame in which the events in question are at rest. In the lightning scenario, because the lightning bolts take place in the embankment frame, the embankment frame is privileged. In the scenario of the light flashing in the center of the train and reaching the front and back of the train, the measurement of events from the train frame (simultaneous) is correct while the measurement of events from the embankment frame (back prior to front) is incorrect. Rather than posit different times for each frame, we recognize that both frames share the same present moment but that only one frame gives the correct reading. The relativity of simultaneity is subjective. Given that the distortion is caused by the speed of light, we might even call it an optical illusion.

Yet time dilation is an indisputable fact. The question then becomes this: how do we account for time dilation in the context of universal simultaneity?

Staff: Mentor

Because they are at rest in that frame. The lightning bolts are at rest in the embankment frame and in motion in the train frame (because the train is moving relative to the lightning bolts).

Ah, now I see what you're thinking. But don't confuse the speed of the light source (which makes sense, but is irrelevant) with the speed of the event of the lightning striking the end of the train (which makes no sense).

What if the lightning strikes occurred at different times? Just because the lightning source (cloud) is at rest with respect to the embankment does make the strikes simultaneous in that frame.

What if instead of lightning there were giant flash bulbs at the ends of the train? Those bulbs move along with the train, but it is certainly possible for them to flash at the same time with respect to the embankment frame.

What if the lightning strikes occurred at different times? Just because the lightning source (cloud) is at rest with respect to the embankment does [not] make the strikes simultaneous in that frame.

Of course. The strikes don't have to be equidistant from the embankment. Einstein uses the example of simultaneity within one frame and its absence in a different frame to illustrate the lack of simultaneity across frames.

My claim is that simultaneity does indeed apply across frames. Only in the abstract does the dismissal of a universal frame of reference (fixed aether) make all frames equally relative. In reality, that is, as soon as something actually happens, a privileged frame presents itself, namely the frame in which the disputed events occur. If the scenario is lightning, the privileged frame is the embankment. If the scenario is a flash of light in the train, the privileged frame is the train. Instead of two frames equally valid and therefore each in possession of its own time, we have one correct and one incorrect frame (per scenario) in the context of a single present moment. Multiple times (relative simultaneity) cannot be inferred from multiple frames.

Einstein's approach works only if we can assume away flowing time from the outset. In this case there's no such thing as "happening" and therefore no difference between abstraction and reality. So long as the equality of all frames is true in the abstract, it's true, period. This is why Popper called Einstein Parmenidean. Like Zeno, another student of Parmenides, Einstein banished movement and change, but he did so by the much more fundamental means of recasting time as static dimensionality.

Incidentally, in a universe that's actually happening, simultaneity across frames is the only way we can account for time dilation. Otherwise, in relation to low-speed frames, the high-speed frame literally would regress into the past due to time slowing, a problem Einstein evaded by eliminating temporality altogether. No flow no slow.

Staff: Mentor

If the scenario is lightning, the privileged frame is the embankment. If the scenario is a flash of light in the train, the privileged frame is the train

What if a single lightning bolt hits an end of the train and the embankment together while another does the same at the other end? We could imagine the bolts striking the exact point where the wheel of the train touches the rails, leaving a scorch mark on the rails and triggering a flash on the train.

Now we have a flash at one end of the train, and everyone on the train and the ground agrees that the flash happened at exactly the same time and place that the scorch mark on the rails was created. And we can say the same thing about the lightning strike, flash, and scorch mark at the other end of the train.

But if the train guys say the two lightning bolts struck at the same time, the ground guys will say they struck at different times, and vice versa. So why should we say that one of them is more right than the other?

I'm sure you don't realize this, but claiming that the timing of events in one frame is definitive while in another frame is distorted, can only be true if you believe in a privileged frame, such as a "luminiferous aether" and that you can identify which frame it is.

But your claim behooves you to now identify the universal frame of reference, as you say the fixed aether. Are you up to it?

In reality, that is, as soon as something actually happens, a privileged frame presents itself, namely the frame in which the disputed events occur. If the scenario is lightning, the privileged frame is the embankment. If the scenario is a flash of light in the train, the privileged frame is the train. Instead of two frames equally valid and therefore each in possession of its own time, we have one correct and one incorrect frame (per scenario) in the context of a single present moment. Multiple times (relative simultaneity) cannot be inferred from multiple frames.

Suppose we have two materials that explode on impact. One of these is located on a pedestal on the top of a moving train car and the other one is hanging from a bridge anchored on the embankment. The impact causes a flash of light that expands spherically from the point of impact. An observer riding on the car at the point of impact will observe that he is in the center of that expanding sphere of light. An observer located on the bridge at the point of impact will also observe that he is at the center of that expanding sphere of light. How do you determine which is the privileged, correct frame?